Hybrid elements

A hybrid element formulation is available for just about every type of continuum element in Abaqus/Standard, including all reduced-integration and incompatible mode elements. Hybrid elements are not available in Abaqus/Explicit. Elements using this formulation have the letter “H” in their names.

Hybrid elements are used when the material behavior is incompressible (Poisson's ratio = 0.5) or very close to incompressible (Poisson's ratio > 0.475). Rubber is an example of a material with incompressible material behavior. An incompressible material response cannot be modeled with regular elements (except in the case of plane stress) because the pressure stress in the element is indeterminate. Consider an element under uniform hydrostatic pressure (Figure 1).

Figure 1. Element under hydrostatic pressure.

If the material is incompressible, its volume cannot change under this loading. Therefore, the pressure stress cannot be computed from the displacements of the nodes; and, thus, a pure displacement formulation is inadequate for any element with incompressible material behavior.

Hybrid elements include an additional degree of freedom that determines the pressure stress in the element directly. The nodal displacements are used only to calculate the deviatoric (shear) strains and stresses.

A more detailed description of the analysis of rubber materials is given in Materials.